Add the following rational expressions. $\dfrac{k^3}{k+5}+\dfrac{7k^3+3}{k+5}=$
Answer: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{k^3}{k+5}+\dfrac{7k^3+3}{k+5} \\\\ &=\dfrac{(k^3)+(7k^3+3)}{k+5} \\\\ &=\dfrac{k^3+7k^3+3}{k+5} \\\\ &=\dfrac{8k^3+3}{k+5} \end{aligned}$ In conclusion, $\dfrac{k^3}{k+5}+\dfrac{7k^3+3}{k+5}=\dfrac{8k^3+3}{k+5}$